Not trying to be nitpicky or anything, I'm honestly not 100% certain, but I thought the Romulans were in the Beta Quadrant?

Yes, they are, but it's a long-standing custom in onscreen Trek to use "Alpha Quadrant" as a shorthand for "the territory of the Federation and its neighbors, which is mostly in the Alpha Quadrant but extends into the Beta Quadrant as well." It's much the same as how Europe is considered part of "the West" even though most of it is in the Eastern Hemisphere.